A Predicted Mathematical Cancer Tumor Growth Model of Brain and Its Analytical Solution by Reduced Differential Transform Method

Gandhi, Hemant; Tomar, Amit; Singh, Dimple

doi:10.1007/978-981-15-5414-8_17

Cited by 11 publications

(7 citation statements)

References 12 publications

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“…Jafari et al [16] explored the numerical scheme to study the system of fractional PDEs. Gandhi et al [30][31][32][33][34] provided the explicit solution of fifth-order and fourth-order fractional systems by Lie symmetry analysis. He has been discussed about brain cancer tumor growth model and its analytic solution by the application of fractional reduced differential transform method on Burgess equation.…”

Section: Introductionmentioning

confidence: 99%

Application of Symmetry Analysis and Conservation Laws to Fractional-Order Nonlinear Conduction-Diffusion Model

Dhull,

Tomar,

Gandhi

et al. 2024

Preprint

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This study is aimed to perform Lie symmetry analysis of the nonlinear fractional-order conduction-diffusion Buckmaster model (BM), which involves the Riemann-Liouville (R-L) derivative of fractional-order ‘β’. We are going through symmetry reduction to convert the fractional partial differential equation into a fractional ordinary differential equation. The fractional derivatives of the converted differential equations are evaluated with the help of Erdelyi-Kober (E-K) fractional operators. The power series solution and its convergence are analyzed with Implicit theorem. Conservation laws of the physical model are obtained for consistency of system by Noether’s theorem.

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Section: Introductionmentioning

confidence: 99%

Application of Symmetry Analysis and Conservation Laws to Fractional-Order Nonlinear Conduction-Diffusion Model

Dhull,

Tomar,

Gandhi

et al. 2024

Preprint

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“…In the current research, there have been fast development in the field of fractional order systems involving in science, engineering and technology i.e. bioscience, fluid flow, electromagnetic, viscoelasticity, pandemic analysis, medicine, infectious modeling, drug therapy, image processing and diffusion wave equations [9,10,15,16,32].…”

Section: Introductionmentioning

confidence: 99%

Conservation Laws and Explicit Solution of system of Fractional-Order Coupled Nonlinear Hirota Equations by Lie Symmetry Analysis

Gandhi,

Tomar,

Singh

2024

Preprint

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The main objective of this research article is to summarize the study of the application of Lie symmetry reduction to the fractional-order coupled nonlinear complex Hirota system of partial differential equations. By the efficient use of symmetries and explicit solutions, this system reducing to nonlinear fractional ordinary differential equations (FODEs) with the application of Erdyli-Kober (E-K) operators for fractional derivatives and integrals depending on real order. Investigating the convergent series solution along with adjoint system and providing the conservation laws by Noether’s theorem.

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“…Although they can infect other organs, the cancer cells that spread to other body regions are identical to the original ones. For instance, if lung cancer spreads to the liver, the cancer cells there are still lung cancer cells [2][3][4].…”

Section: Introductionmentioning

confidence: 99%

“…With help of q-HAM, find answer of the time-fractional partial differential equation. Gandhi H et al [2] says that the situation where net death rate & tumor growth are considered & therapy is time-dependent. To find model's solution, the fractional RDT method was used.…”

Section: Introductionmentioning

confidence: 99%

An investigation of the complexities of a malignant tumor's fractional-order mathematical model

Singh¹,

Gupta²,

Mishra³

2022

Proceedings of the Seventh International Conference on Research in Intelligent and Computing in Engineering

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4In this paper, model of a malignant tumor & associated problems are examined using fractional-order method. We consider a case where the malignant tumor cells' net death rate is solely time-dependent. Fractional homotopy decomposition method (HDM) has been applied to determine model's series solution. The answer to the HDM is given using the Maclaurin expansion. This method's use of the Mathematica software package allows for fast and simple computation of series solutions, which is one of its benefits.

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A Predicted Mathematical Cancer Tumor Growth Model of Brain and Its Analytical Solution by Reduced Differential Transform Method

Cited by 11 publications

References 12 publications

Application of Symmetry Analysis and Conservation Laws to Fractional-Order Nonlinear Conduction-Diffusion Model

Application of Symmetry Analysis and Conservation Laws to Fractional-Order Nonlinear Conduction-Diffusion Model

Conservation Laws and Explicit Solution of system of Fractional-Order Coupled Nonlinear Hirota Equations by Lie Symmetry Analysis

An investigation of the complexities of a malignant tumor's fractional-order mathematical model

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